Article pubs.acs.org/JPCC
Extinction vs Absorption: Which Is the Indicator of Plasmonic Field Strength for Silver Nanocubes? Rachel Near, Steven Hayden, and Mostafa El-Sayed* School of Chemistry and Biochemistry, Georgia Institute of Technology, 901 Atlantic Drive, Atlanta, Georgia 30332, United States S Supporting Information *
ABSTRACT: This investigation demonstrates the contributions of absorption and scattering to the extinction spectrum of silver nanocubes with multipole resonances and the complexity of the resulting plasmon field strengths for these varying modes. The three-dimensional plasmonic field distribution and orientation around a silver nanosphere (AgNS; 40 nm) and a silver nanocube (AgNC; 40, 60, 86 nm) were calculated in the visible via the discrete dipole approximation. The three-dimensional nature of these particles allows for significant contribution from the quadrupole mode in some cases. The AgNS displays one plasmon band, its dipole mode, and has little contribution from scattering. The maximum plasmon field occurs at the extinction maximum, as expected. The 40 nm AgNC exhibits multiple plasmon bands, and the highest maximum field strength is attained from excitation of the quadrupole mode, not the dipole mode. As the size of the AgNC increases, the contribution from scattering increases. When the contribution from scattering is greater than the contribution from absorption in a AgNC, the field strength within a plasmon mode trends with the absorption and not with the extinction or scattering. This should be considered in applications of AgNCs, as excitation of the largest peak in the experimental extinction spectrum will not always result in the strongest plasmon field strength.
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by an external field. The response of the point dipoles to the external field and to one another is solved self-consistently using Maxwell’s equations. The DDSCAT 6.1 code offered publicly by Draine and Flatau25 allows for calculation of the absorption and scattering spectra separately, allowing for assessment of the contributions from each to the extinction spectra, which is the sum of these two components. Furthermore, with modifications to the code by Goodman26 and Schatz,27 it is possible to calculate the electric field enhancement contours and the individual dipole orientations at a specific wavelength. These plots can only be generated for one slice through the particle at a time, but the slice position can be chosen. Thus, by repeating the calculations for multiple slices through the particle, a three-dimensional representation of the field can be obtained at a particular resonance wavelength. Using DDA, we calculate the absorption and scattering components of the extinction as well as the three-dimensional field plots for whole particles. We show that an in-depth investigation of the three-dimensional field enhancement contours is needed to accurately assign the plasmonic modes and determine which wavelength results in the largest field enhancement for silver nanocubes. We also elucidate the relationship between the absorption spectrum and maximum field enhancement within a single plasmon mode for a silver nanosphere and for silver nanocubes of varying size.
INTRODUCTION Plasmonic nanoparticles can interact with light in several different ways. The amount of light scattered by a particle relative to the amount of light absorbed by the particle is dependent on the particle’s size, shape, and composition.1−3 Scattering of light by plasmonic particles is the key process in many diagnostic applications employing nanoparticles, as the large amount of scattering makes it easy to see the particles via dark field microscopy.1,4−9 Many other applications (e.g., solar cells,10−12 photothermal therapy,8,13−15 and drug delivery13,16−18) rely heavily on the absorption of light by plasmonic particles and the subsequent conversion of that energy to heat or strong electric fields. In many applications involving the use of electric fields around nanoparticles, a specific wavelength or selection of wavelengths is used to excite the particle to give the strongest field. It has been shown elsewhere that excitation at the dipolar plasmon wavelength creates very strong fields,19,20 and many applications exploit this, choosing wavelengths based on the largest peak from the experimentally collected extinction spectrum. Our results for silver nanocubes indicate that field strength trends with absorption and not extinction or scattering, which necessitates a thorough theoretical investigation to accurately determine the ideal excitation wavelength for applications. The discrete dipole approximation (DDA) is a theoretical technique for modeling the spectral properties of systems. DDA has the advantage of being able to model particle(s) of arbitrary shape.1,20−24 In this method, the particle is represented by a three-dimensional finite lattice of point dipoles that is excited © 2012 American Chemical Society
Received: September 18, 2012 Revised: October 10, 2012 Published: October 11, 2012 23019
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METHODS The optical response of a silver sphere (40 nm diameter) and a silver nanocube with varying edge length (40, 60, and 86 nm) was calculated using the DDA method with the DDSCAT 6.1 code offered publicly by Draine and Flatau25 with modifications by Goodman26 and Schatz.27 The dielectric values for silver reported by Johnson and Christy28 were used. The incident light is always polarized left to right along the edge of the AgNC in this report, and the medium surrounding the particle was represented as water with a refractive index of 1.333.
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RESULTS AND DISCUSSION A. 40 nm Silver Nanosphere. The extinction, absorption, and scattering spectra for a 40 nm AgNS in water are shown in Figure 1a. Here, there is only one plasmon band, which has Figure 2. Three-dimensional representation for the electric field enhancement of a 40 nm AgNS when excited with a wavelength of 393 nm. The field location and field vector orientations indicate that this is the dipole mode.
scale. The maximum enhancement for this wavelength is 1085 and occurs on the middle slice of the particle. A summary of the spectral and field information for the 40 nm AgNS is plotted in Figure 1b. In addition to the field contour, a plot of the individual dipoles that make up the particle and their orientation was generated for each particle slice. Hereafter, a minus sign will be used to represent when the field vectors are pointing away from an area. Conversely, a plus sign will be used to represent when the field vectors are all pointing toward an area (Supporting Information Figure S1). The composite field plot for the AgNS at 393 nm has the field vectors pointing away from the left side and toward the right side throughout the entire particle. This corresponds to the most primitive dipole mode for the particle, which is the largest extinction peak. Similar investigations were carried out slightly off resonance at 388 and 398 nm (Supporting Information Figures S2 and S3). The field location and orientation are the same as that seen at 393 nm; these two wavelengths also correspond to the dipole mode. The spectral values and field intensities for all three wavelengths are plotted in Figure 1b, and the highest field enhancement is found where the maximum extinction and absorption values occur at 393 nm. In the case of the 40 nm silver nanosphere, we see that the three-dimensional field modeling can be used to accurately assign different plasmon modes based on the field contour and orientation. Additionally, the field maximum occurs at the absorbance maximum, which in this case coincides with the extinction maximum, as there is very little contribution from scattering. B. 40 nm Silver Nanocube. Next, we wanted to use this three-dimensional field mapping to examine particles with more complex spectral features. It has previously been shown that silver nanocubes (AgNCs) exhibit multiple spectral peaks and can have a significant contribution from scattering when the AgNC is of sufficient size (>30 nm).29−32 Therefore, we first considered a silver nanocube (AgNC) with a 40 nm edge length. The DDA extinction (black), absorption (red), and scattering (green) spectra for a 40 nm AgNC are shown in Figure 3a. At this size, absorption dominates scattering, but
Figure 1. (a) DDA extinction (black), absorption (red), and scattering (green) spectra for a 40 nm AgNS in water. (b) Comparison of spectral value trends with field enhancement trends for the dipole mode of a 40 nm AgNS. It can be seen that the maximum in field strength corresponds to the maximum spectral values.
some contribution from scattering but is dominated by absorption. The maximum of this plasmon band occurs at 393 nm. To accurately assign the plasmon modes, multiple field contour plots were generated at each wavelength for five evenly spaced slices through the particle. When combined (as in Figure 2), these five slices give a good three-dimensional representation of the field location and orientation at a particular resonance wavelength. The composite field plot at 393 nm is shown in Figure 2 along with its field enhancement 23020
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Figure 4. Three-dimensional representation for the electric field enhancement of a 40 nm AgNC when excited with a wavelength of 475 nm. The field locations and field vector orientations indicate that this is the dipole mode.
at the corners of the particle in each slice. Also, the orientation of the field vectors corresponds to the most primitive dipole mode for the particle; this is also the largest extinction peak occurring furthest to the red. The next two wavelengths considered for the 40 nm AgNC were 482 and 487 nm (Supporting Information Figures S4 and S5, respectively). Both wavelengths have the same field location and orientation as was seen for 475 nm, meaning both 482 and 487 nm also correspond to the dipole mode for the 40 nm AgNC. There is an increase in the field enhancement maximum from 475 to 482 nm and a decrease from 482 to 487 nm, with corresponding trends in the spectral values (Figure 3b). Next, we considered the band at 435 nm. Unlike what has been seen previously, the field orientation is not the same for all five slices (Figure 5). Here, the top and bottom of the particle have the same field orientation, with the field vectors pointing away from the left and toward the right, while the interior of the particle has the opposite field vector orientation, pointing away
Figure 3. (a) DDA extinction (black), absorption (red), and scattering (green) spectra for a AgNC in water with a 40 nm edge length. Higher order modes are present, but the modes are well separated. Absorption dominates scattering. (b) Comparison of spectral value trends with field enhancement trends for the dipole mode of a 40 nm AgNC. The maximum field strength occurs at the spectral maxima, which all coincide. (c) Comparison of spectral value trends with field enhancement trends for the quadrupole mode of a 40 nm AgNC. The maximum field strength occurs at the spectral maxima, which all coincide.
there is still a substantial contribution from scattering. It is also apparent that there are multiple bands, though at this size they are reasonably well separated. The first wavelength investigated was 475 nm, which is slightly off resonance for the peak appearing furthest to the red. The composite field plot for 475 nm is shown in Figure 4. It can be seen that the field is located
Figure 5. Three-dimensional representation for the electric field enhancement of a 40 nm AgNC when excited with a wavelength of 435 nm. The field location and field vector orientations indicate that this is the quadrupole mode. 23021
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from the right and toward the left. These field orientations suggest a quadrupole mode. The wavelengths 440 and 445 nm were both found to correspond to the quadrupole mode, as indicated by their composite field plots shown in the Supporting Information (Figures S6 and S7). For the 40 nm AgNC, the field enhancement maximum increases from 435 to 440 nm and then decreases from 440 to 445 nm with corresponding trends in the spectral values (Figure 3c). It is interesting to note that the maximum field enhancement for the quadrupole mode is greater than what is seen for the dipole mode. C. 60 nm Silver Nanocube. The 40 nm AgNC allows for investigation of multiple modes, but the spectra are still fairly simple; the modes are well separated from one another, and absorption still dominates scattering. Next we considered an even larger silver cube (60 nm) to increase the contribution from scattering (Figure 6a).1−3 By comparison with the spectra for the 40 nm AgNC (Figure 3a), there is considerably higher contribution from scattering than was seen for the smaller particle, as expected. Despite the increase in contribution from scattering, the multiple bands still remain fairly well distinguished. It was found that wavelengths 433, 441, and 443 nm all corresponded to the quadrupole mode for the 60 nm AgNC, as indicated by their composite field plots (Figures 7, S8, and S9). However, an interesting trend was observed for the field strength. It can be seen in Figure 6c that the field increases from 433 to 441 nm and reaches a maximum at 443 nm. The absorption value follows the same trend as the field strength maximum, increasing from 433 to 443 nm, while the extinction and scattering values do not. Thus, for this particle whose scattering contributes more to the extinction than the absorption does, the absorption value is a better indicator of field strength within a single plasmon mode than is the extinction. Next, we examined the dipole mode at 492, 495, and 505 nm (Figures 8, S10, and S11). Again we see that the field strength trends with the absorption and not with the scattering or extinction for this plasmon mode (Figure 6b). D. 86 nm Silver Nanocube. Finally, an even larger AgNC (86 nm) was studied to see if the plasmon modes could be distinguished despite a further increase in scattering as well as to further investigate the relation between field enhancement and absorption. For this particle, the scattering dominates the absorption to the point that the different plasmon bands begin to overlap in the extinction spectrum (Figure 9a). Here, more modes than the quadrupole and dipole were considered to determine the robustness of the three-dimensional particle composite field plot in distinguishing between modes. The data are presented in detail in the Supporting Information (Table S1) and discussed forthwith. D.1. Higher order multipoles. It was found that the wavelengths 377.5, 405, 417, and 440 nm all corresponded to distinct higher order plasmon modes (Figures 10, 11, 12, and 13), as indicated by their complex but distinct field locations and field vector orientations. These results show that the threedimensional modeling can be applied to distinguish between even very complicated higher order plasmon modes. D.2. Quadrupole and Dipole Modes. The wavelengths 443, 447, 454, and 462 nm were all found to correspond to the quadrupole mode (Figures 14, S12, S13, and S14), as indicated by the field contour and field vector orientations. As was previously seen, the maximum field strength trends with the
Figure 6. (a) DDA extinction (black), absorption (red), and scattering (green) spectra for a AgNC in water with a 60 nm edge length. Higher order modes are present, but the modes are well separated. Scattering dominates absorption. (b) Comparison of spectral value trends with field enhancement trends for the dipole mode of a 60 nm AgNC. The maximum field strength trends with the absorption, not the scattering or extinction. (c) Comparison of spectral value trends with field enhancement trends for the quadrupole mode of a 60 nm AgNC. The maximum field strength trends with the absorption, not the scattering or extinction.
absorbance and not with the scattering or extinction values (Figure 9b). The wavelengths 470.5 and 487 nm were found to correspond to a different mode that is a mixture of the quadrupole and dipole modes (Figures 15 and S15). For this mode, if only the field enhancement locations had been considered, then it might appear that this wavelength represented the same mode as the previous four (443, 447, 23022
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Figure 7. Three-dimensional representation for the electric field enhancement of a 60 nm AgNC when excited with a wavelength of 433 nm. The field location and field vector orientations indicate that this is the quadrupole mode.
Figure 9. (a) DDA extinction (black), absorption (red), and scattering (green) spectra for a AgNC in water with an 86 nm edge length. Higher order modes are present, and there is considerable overlap between the modes. Scattering dominates absorption. (b) Comparison of spectral value trends with field enhancement trends for the quadrupole mode of an 86 nm AgNC. The maximum field strength trends with the absorption, not the scattering or extinction. Figure 8. Three-dimensional representation for the electric field enhancement of a 60 nm AgNC when excited with a wavelength of 492 nm. The field location and field vector orientation indicate that this is the dipole mode.
454, and 462 nm). Similarly, if only the top slice had been considered, which shows the strongest field enhancement in all cases, this mode would have appeared to be the quadrupole mode even if the dipole orientations had also been considered. These results in particular show the importance of basing mode assignments on thorough theoretical results. Finally, we examined 523 nm, which corresponds to the maximum of the large extinction peak. Here, the location of the field is focused at the corners, and the field vectors are pointing away from the left and toward the right throughout the entirety of the particle (Figure 16). This corresponds to the most primitive dipole mode for the particle, which agrees with the fact that this is also the largest extinction peak. Interestingly, the maximum field enhancement is only 6400, which is an order of magnitude less than that seen for the last 7 wavelengths. Although 523 nm corresponds to large peak in the extinction and scattering (Figure 9a), there is very little contribution from the absorption, and thus there is little field enhancement. This agrees with our previous results that indicate the absorption is
Figure 10. Three-dimensional representation for the electric field enhancement of an 86 nm AgNC when excited with a wavelength of 377.5 nm. The field locations and field vector orientations indicate that this is a higher order multipole mode.
one of the key factors in determining which mode will give the highest field enhancement for AgNCs. 23023
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Figure 14. Three-dimensional representation for the electric field enhancement of an 86 nm AgNC when excited with a wavelength of 443 nm. The field locations and field vector orientations indicate that this is the quadrupole mode.
Figure 11. Three-dimensional representation for the electric field enhancement of an 86 nm AgNC when excited with a wavelength of 405 nm. The field locations and field vector orientations indicate that this is a higher order multipole mode.
Figure 15. Three-dimensional representation for the electric field enhancement of an 86 nm AgNC when excited with a wavelength of 470.5 nm. The field locations and field vector orientations indicate that this is a hybrid between the quadrupole and dipole modes.
Figure 12. Three-dimensional representation for the electric field enhancement of an 86 nm AgNC when excited with a wavelength of 417 nm. The field locations and field vector orientations indicate that this is a higher order multipole mode.
Figure 16. Three-dimensional representation for the electric field enhancement of an 86 nm AgNC when excited with a wavelength of 523 nm. The field locations and field vector orientations indicate that this is the dipole mode.
Figure 13. Three-dimensional representation for the electric field enhancement of an 86 nm AgNC when excited with a wavelength of 440 nm. The field locations and field vector orientations indicate that this is a higher order multipole mode. 23024
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representative field vector plot; specifically, a representative field vector plot (Figure S1); composite field plots for the 40 nm AgNS at wavelengths 388 and 398 nm (Figures S2 and S3, respectively); composite field plots for the 40 nm AgNC at wavelengths 482, 487, 440, and 445 nm (Figures S5, S6, and Figure S7, respectively); composite field plots for the 60 nm AgNC at wavelengths 441, 443, 495, and 505 nm (Figures S8, S9, S10, and S11, respectively); composite field plots for the 86 nm AgNC at wavelengths 447, 454, 462, and 487 nm (Figures S12, S13, S14, and S15, respectively), with a summary of results in Table S1. This material is available free of charge via the Internet at http://pubs.acs.org.
In the case of silver nanocubes, we see we can accurately assign multiple plasmon modes from more complicated spectra using the three-dimensional field modeling. As the contribution from scattering increases (i.e., as the size of the AgNC increases), it becomes apparent that the field strength depends on the absorption and not the extinction or scattering.
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CONCLUSIONS We have completed a thorough and systematic investigation of the plasmon modes of a 40 nm AgNS and various sizes of AgNCs. Our results show that there are multiple distinct plasmon modes for AgNCs, and specifically that there is a significant contribution to the spectra from the quadrupole and dipole modes. We also showed that consideration of the field distribution and orientation in three dimensions is necessary for accurate description and assignment of the plasmon modes for AgNCs. We found for all three AgNC sizes considered that the quadrupole mode results in a higher maximum field enhancement than the dipole mode. Further, we found an interesting relationship between the spectral values and field intensity for the AgNCs. Specifically, when the contribution from scattering is greater than that from absorption, the field strength within a plasmon mode of a AgNC trends with the absorption values and not with the extinction or scattering. It seems safe to conclude that this is always the case for AgNCs. However, when there is a small contribution from scattering, this distinction becomes less necessary, as the extinction and absorption peaks become more coincidental. Experimentally, it is typically the extinction spectrum that is collected, and this could be misleading in choosing the resonance wavelength for maximum field enhancement of AgNCs if there is a significant contribution from scattering (e.g., in large AgNCs). We should now point out that the relationship between absorption and field strength is not absolute but only can be used within one mode for one particle at a time. This means that for the same mode in two different-sized AgNCs, a higher absorption value for one particle size does not necessarily indicate a higher maximum field enhancement for that particle compared to the other. Second, the absorption values cannot be compared between modes within a single AgNC to determine which will have a higher field. In fact, our results for all three sizes of AgNC considered show that the quadrupole mode results in the highest maximum field enhancement, not the dipole mode, even though in some cases the absorption value for the dipole peak was higher than the quadrupole peak. All these trends simply point out that a thorough theoretical investigation is needed to accurately assign the plasmon modes and choose the wavelength most appropriate for applications using AgNCs. All in all, our results indicate that plasmon field strength of AgNCs trends with absorption, which indicates the necessity of thorough theoretical investigation to choose the appropriate wavelength for maximum field enhancement for applications using AgNCs. This is especially true for particles with a significant quadrupole mode and/or a substantial contribution from scattering
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AUTHOR INFORMATION
Corresponding Author
*Phone: 404-894-0292. Fax: 404-894-7452. E-mail: melsayed@ gatech.edu. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the AFOSR Center of Excellence on BIONIC under grant No FA9550-09-1-0162 and AFRL/RX. REFERENCES
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ASSOCIATED CONTENT
S Supporting Information *
Additional composite field plots for the 40 nm AgNS, 40 nm AgNC, 60 nm AgNC, and 86 nm AgNC as well as a table summarizing the results for the 86 nm AgNC and a 23025
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